THE FOEMATION OF CONDENSED CORRELA- 

 TION TABLES WHEN THE NUMBER OF 

 COMBINATIONS IS LARGE 



DR. J. ARTHUR HARRIS 

 Carnegie Institution op Washington 



After the principles of any method of research are 

 laid down by those who have the genius or the good for- 

 tune to make fundamentally new contributions, there 

 always remains much to be done in the refinement, simpli- 

 fication, or adaptation of methods to render them most 

 practically applicable in the routine of investigation. 

 This is especially, true in the modern higher statistics, 

 where, at the very best, the labor is excessive. 



One of the most onerous of the statistical processes is 

 the determination of correlation in cases in which each 

 individual measurement must be weighted by comparison 

 with a series of others. In an earlier number of this 

 journal 1 a method was described for the rapid formation 

 of the heavy intra-class and inter-class 2 correlation and 

 contingency surfaces by the use of a machine permitting 

 simultaneous multiplication and summation. Methods 

 of dealing with such correlations without the formation 

 of tables will be published later. But abstract formula? 

 in the hands of inexperienced calculators are apt to lead 

 to erroneous constants, which in the absence of the orig- 

 inal data can never be corrected. Again, the va ] i d i t y ■ , f* 

 the correlation coefficient as a measure of interdepend- 

 ence depends largely upon linearity of regression. Hence, 

 tables should be given whenever possible. The purpose 

 of this note is to show how, in the case of relationships 



